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GRADING AND SCREENING                               247
increases, should be proportional to the size of the material fed. It should not be greater than three times the diameter of the largest grain fed though it frequently is in screening fine sizes because of practical considerations. If the stroke is too great there is apt to be no screening effect except towards the end of it when the grains are coming to rest. If a grain >{oo in. diameter is passing over a screen with Mo in. openings and the length of stroke be 50 mesh lengths long then evidently there is little or no screening effect until towards the end of the stroke when the grain is coming to rest. If coarse crushed grains are being screened the coarsest of them being say in the neighborhood of 1 in. diameter then evidently a stroke of about Mo in. while yielding some slight screening effect would not give little capacity. On the other hand a stroke in the neighborhood of an inch would give good screening effect and a large capacity. To^equalize the capacity factor in the two cases the screen with Mo in. opening would have to have 50 times the number of strokes that would be required for screening the • coarser material. If coarse material is being screened on a shaking screen with 1-in. opening at the rate of 300 strokes per minute of 1-in. length then as must be evident other things being equal and an equal quality of screening work being desired a screen of Mo in. must have 15,000 strokes per minute if it be desired to equalize the advance factor of capacity. It is true that if this is done that the finer grains will pass over 50 times as many apertures as the coarser ones but under the chance law the elements of. which have been recited at length, the fine grains will need just this proportionately greater number of apertures to cross in order that the screen work may be as good with the fine size as the coarse.
As indicated at an earlier point the capacity of a flat screen cannot be greater than would bring a single line of contiguous oversize grains to the discharge point of the screen consequently if A is the average of the width of the two openings of the two screens involved in producing a grading, the one through which it has passed and the one over which it is passing, expressed in a fraction of a foot, then theoretically the capacity cannot exceed in cubic feet per hour per foot of screen width more than
5AR •p-
R being the rate of advance of material in inches per minute and P the percentage expressed decimally that the oversize bears to the whole weight of material fed to the screen and which would have to be determined experimentally by screen or other test and of which if done the first would be only a practical approximation. Printed figures on the comminution of various substances showing the proportion of oversizes to be expected from any degree of comminution can be used.
A little reflection will show that the capacity will depend upon the proportion of oversize, the greater it is the less the capacity of the screen and the greatness of the drop in size of screen opening from one screen to another. As an example of the application of the formula the capacity under it of a screen with %-in. opening will be considered, being fed ore or rock crushed to pass an inch-square opening. The screen is assumed to be of the flat shaking type and have imparted to it 300 differential strokes of 1 in. each per minute. Here A is the average of 1 in. and % in. or expressed in a fraction of a foot, 0.073, and R, 300. Experience with rocks and ores show that the screen ratio as used in this example which is close to 1.414 the oversize of a M-in. screen will be about 27 per cent of the weight fed to it. The capacity of the formula under the assumptions and making the proper substitutions becomes 406 cu. ft. per hour.
Tonnage Capacity per Foot of Width, Flat Screening Surface, Rocks and Ores.—These substances in solid masses can be assumed to weigh 165 Ib. per cubic foot. But as shown on pages 235 and 236 they occupy when crushed only about 40 per cent of the cube whose edge is the size of aperture through which fragments of them will iust pass. The factor for multiplying cubical capacity for